# Describe a use for the Remainder Theorem.

Question
Polynomial division
Describe a use for the Remainder Theorem.

2021-03-09
Concept used:
Remainder theorem states that “If a polynomial f(x)is divided by x — k, then the remainder is the value f(k)”
We can use polynomial division to evaluate polynomials using the Remainder Theorem. If the polynomial is divided by x - k, the remainder is r, then this value equals the value of the polynomial function at k, that is, f(k). So this helps to evaluate the polynomial at a given value of x. Since the division is done by a linear factor, we can use the synthetic division method.

### Relevant Questions

Discuss the following situation by computation or proving. Make sure to show your complete solution.
Give a polynomial division that has a quotient of x+5 and a remainder of -2.
Consider the polynomial Division $$\frac{x^{3}+5x^{2}-7x−4}{x−2}$$
The correct Answer is: hint the answers contains $$x^{2}$$, x, and it has a remainder.
Discuss the following situation by computation or proving.
Make sure to show your complete solution.
Give a polynomial division that has a quotient of $$x+5$$ and a remainder of -2.
Discuss the following situation by computation or proving. Make sure to show your complete solution. Give a polynomial division that has a quotient of $$x+5$$ and a remainder of -2.
Give a polynomial division that has a quotient of x+5 and a remainder of -2
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $$\frac{x^{n}-1}{x-1}$$.
Greate a numerical example to test your formula.
$$\frac{x^{4}-1}{x-1}$$
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $$\frac{x^{n}-1}{x-1}$$.
Greate a numerical example to test your formula.
$$\frac{x^{3}-1}{x-1}$$
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $$\frac{x^{n}-1}{x-1}$$.
Greate a numerical example to test your formula.
$$\frac{x^{2}-1}{x-1} =$$ ?

Use long division to rewrite the equation for g in the form
$$\text{quotient}+\frac{remainder}{divisor}$$
Then use this form of the function's equation and transformations of
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
to graph g.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}+{7}}}{{{x}+{3}}}}$$

$$\text{quotient}+\frac{remainder}{divisor}$$
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}$$